<h2>DESCRIPTION</h2>

<em>r.resamp.filter</em> resamples an input raster, filtering the
input with an analytic kernel. Each output cell is typically calculated
based upon a small subset of the input cells, not the entire input.
<em>r.resamp.filter</em> performs convolution (i.e. a weighted sum is
calculated for every raster cell).

<p>
The module maps the input range to the width of the window function, so
wider windows will be "sharper" (have a higher cut-off frequency), e.g.
lanczos3 will be sharper than lanczos2.

<p>
r.resamp.filter implements FIR (finite impulse response) filtering. All
of the functions are low-pass filters, as they are symmetric. See
<a href="http://en.wikipedia.org/wiki/Window_function">Wikipedia: Window function</a>
for examples of common window functions and their frequency responses.

<p>
A piecewise-continuous function defined by sampled data can be considered
a mixture (sum) of the underlying signal and quantisation noise. The
intent of a low pass filter is to discard the quantisation noise while
retaining the signal.

The cut-off frequency is normally chosen according to the sampling
frequency, as the quantisation noise is dominated by the sampling
frequency and its harmonics. In general, the cut-off frequency is
inversely proportional to the width of the central "lobe" of the window
function.

<p>
When using <em>r.resamp.filter</em> with a specific radius, a specific
cut-off frequency regardless of the method is chosen. So while lanczos3
uses 3 times as large a window as lanczos1, the cut-off frequency remains
the same. Effectively, the radius is "normalised".

<p>
All of the kernels specified by the <b>filter</b> parameter are
multiplied together. Typical usage will use either a single kernel or an
infinite kernel along with a finite window.


<h2>NOTES</h2>

Resampling modules (<em>r.resample, r.resamp.stats, r.resamp.interp,
r.resamp.rst, r.resamp.filter</em>) resample the map to match the
current region settings.

<p>
When using a kernel which can have negative values (sinc, Lanczos),
the <em>-n</em> flag should be used. Otherwise, extreme values can
arise due to the total weight being close (or even equal) to zero.

<p>
Kernels with infinite extent (Gauss, normal, sinc, Hann, Hamming,
Blackman) must be used in conjunction with a finite windowing function
(box, Bartlett, Hermite, Lanczos).

<p>
The way that Lanczos filters are defined, the number of samples is
supposed to be proportional to the order ("a" parameter), so lanczos3
should use 3 times as many samples (at the same sampling frequency, i.e.
cover 3 times as large a time interval) as lanczos1 in order to get a
similar frequency response (higher-order filters will fall off faster, but
the frequency at which the fall-off starts should be the same). See 
<a href="http://en.wikipedia.org/wiki/File:Lanczos-kernel.svg">Wikipedia: Lanczos-kernel.svg</a>
for an illustration. If both graphs were drawn on the same axes, they
would have roughly the same shape, but the a=3 window would have a longer
tail. By scaling the axes to the same width, the a=3 window has a narrower
central lobe.

<p>
For longitude-latitude locations, the interpolation algorithm is based on
degree fractions, not on the absolute distances between cell centers.  Any
attempt to implement the latter would violate the integrity of the
interpolation method.


<h2>SEE ALSO</h2>

<em>
<a href="g.region.html">g.region</a>,
<a href="r.mfilter.html">r.mfilter</a>,
<a href="r.resample.html">r.resample</a>,
<a href="r.resamp.interp.html">r.resamp.interp</a>,
<a href="r.resamp.rst.html">r.resamp.rst</a>,
<a href="r.resamp.stats.html">r.resamp.stats</a>
</em>

<p>
Overview: <a href="https://grasswiki.osgeo.org/wiki/Interpolation">Interpolation and Resampling</a> in GRASS GIS

<h2>AUTHOR</h2>

Glynn Clements

<!--
<p>
<i>Last changed: $Date$</i>
-->
